4. An Uber driver only provides service in city A and city B dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45

(a) What is the 1-step transition matrix? (Let 1 = City A and 2 = City B) (5 points)

(b) Suppose he is in city B, what is the probability he will be in city A after two trips? (5 points)

(c) After many trips between the two cities, what is the probability he will be in city B? (6 points)]

Consider the 1981 Super Bowl commercial from Schlitz involving a live taste test (Links to an external site.). A group of people took a live taste test as part of a commercial during the Super Bowl. The taste test was sponsored by the beer company Schlitz. Suppose that a taste tester preferring Schlitz is considered a success which occurs with probability .5. In a sample of 50 what is the probability that 25 or more will choose Schlitz as the best beer?

Consider the 1981 Super Bowl commercial from Schlitz involving a live taste test. Suppose that a taste tester preferring Schlitz is considered a success which occurs with probability .5. In a sample of 200 what is the probability that 100 or more will choose Schlitz as the best beer?

Question 4: The time to finish the Abu Dhabi Grand Prix Formula one (F1) motor race is normally distributed with a mean of 106.47 minutes and a standard deviation of 0.376 minutes.

1. What is the probability that the finishing time of a F1 car in the race selected at random at most 106.375 min?
2. Find the probability that the finishing time of a randomly selected F1 car in the race is between 106.375 min and 107.065 min.
3. What is the finishing time (t₀) such that 95% of the F1 racing cars in the population have finishing time at most t₀?
4. The probability that each of the F1 cars will not finish the race for any reason is 0.12. Given that there were 25 qualified F1 cars in a race, find the probability that at most 5 of these cars will not finish the race.

In​ 2008, the per capita consumption of coffee in Country A was reported to be 19.37 pounds. Assume that the per capita consumption of coffee in Country A is approximately normally​ distributed, with a mean of 19.37 pounds and a standard deviation of 4 pounds. Complete parts​ (a) through​ (d) below.

a. What is the probability that someone in Country A consumed more than 13 pounds of coffee in​ 2008?

b. What is the probability that someone in Country A consumed between 6 and 10 pounds of coffee in​ 2008?

c. What is the probability that someone in Country A consumed less than 10 pounds of coffee in​ 2008?

d. 98​% of the people in Country A consumed less than how many pounds of​ coffee? The probability is 98​% that someone in Country A consumed less than ?? pounds of coffee.

A population of male university students has a distribution of
weights and heights that follow a bivariate normal distribution. The distribution of weights
it has an average of 72 kg and a standard deviation of 8 kg. The height distribution has an average of 170 cm and deviation
standard 10 cm. The correlation coefficient between weights and heights is 0.8. Using these
information calculate:
a) The probability of a boy's weight being between 70 and 80 kg.
b) The probability that a boy's weight is between 70 and 80 kg since his height is 180
cm.
c) The probability of a boy's height being between 175 and 185 cm.
d) The probability of a boy's height being between 175 and 185 cm given that his weight is 80
kg.

The amount of time that a​ drive-through bank teller spends on a customer is a random variable with a mean mu = 4.9 minutes and a standard deviation sigma = 2.4 minutes. If a random sample of 36 customers is​ observed, find the probability that their mean time at the​ teller's window is

​(a) at most 4.3 ​minutes;

​(b) more than 5.3 ​minutes;

​(c) at least 4.9 minutes but less than 5.7 minutes.

(a) The probability that the mean time is at most 4.3 minutes is ___. ​(Round to four decimal places as​ needed.)

​(b) The probability that the mean time is more than 5.3 minutes is ___. ​(Round to four decimal places as​ needed.)

​(c) The probability that the mean time is between 4.9 minutes and 5.7 minutes is ___ . ​(Round to four decimal places as​ needed.)

Summer high temperatures are distributed normally with a mean of 99.6 and a standard deviation of 3.9. NOTE: Round your z − score to 2 decimal places before calculating a probability.

What is the summer high temperature that is the 84 th percentile of this distribution? 102.9 96.3 103.5 95.7 None of the above

What is the probability that a randomly selected summer day has a high temperature of 101? 0 0.6406 0.3594 0.0594 0.9406

What is the probability that a randomly selected summer day has a high temperature greater than 101? 0.9406 0.3594 0.6406 0 0.0594

What is the probability that a randomly selected group of 19 summer days have a high temperature greater than 101? 0.3594 0.9406 0.6406 0.0594 0

A study showed that 66.4% of occupants involved in a fatal car crash wore seat belts. Of those in a fatal car crash who wore seat belts, 2% were ejected from the vehicle. For those not wearing seat belts, 39% were ejected from the vehicle. Complete parts (a) and (b) below.

(a) Find the probability that a randomly selected person in a fatal car crash who was ejected from the vehicle was wearing a seatbelt.

The probability is _______.
(Type an integer or decimal rounded to four decimal places as needed.)

(b) Find the probability that a randomly selected person in a fatal car crash who was not ejected from the vehicle was not wearing a seatbelt.

The probability is _______.
(Type an integer or decimal rounded to four decimal places as needed.)

The registrar needs to assign section numbers to a group of 10 sophomores, 20 juniors, and 30 seniors. There are three sections with available seats, say section A, B, C. Each section has room for up to 60 students. We will assume that the registrar randomly and independently assigns the students to the sections.

a) What is the probability that all ten sophomores will be assigned to the same section?

b) What is the probability that exactly 15 students will be assigned to section B?

c) Given that exactly 15 students are assigned to section B, what is the probability that these 15 students are all juniors?

d) Given that exactly 15 students are assigned to section B, what is the probability that these 15 students consist of 5 sophomores, 5 juniors, and 5 seniors?